Kempe equivalence of edge-colourings in subcubic and subquartic graphs
Combinatorics
2015-03-17 v2
Abstract
It is proved that all 4-edge-colourings of a (sub)cubic graph are Kempe equivalent. This resolves a conjecture of the second author. In fact, it is found that the maximum degree Delta=3 is a threshold for Kempe equivalence of (Delta+1)-edge-colourings, as such an equivalence does not hold in general when Delta=4. One extra colour allows a similar result in this latter case however, namely, when Delta<=4 it is shown that all (Delta+2)-edge-colourings are Kempe equivalent.
Cite
@article{arxiv.1005.2248,
title = {Kempe equivalence of edge-colourings in subcubic and subquartic graphs},
author = {Jessica McDonald and Bojan Mohar and Diego Scheide},
journal= {arXiv preprint arXiv:1005.2248},
year = {2015}
}
Comments
15 pages, 7 figures